We propose a model-based reinforcement learning (RL) approach for noisy time-dependent gate optimization with improved sample complexity over model-free RL. Sample complexity is the number of controller interactions with the physical system. Leveraging an inductive bias, inspired by recent advances in neural ordinary differential equations (ODEs), we use an auto-differentiable ODE parametrised by a learnable Hamiltonian ansatz to represent the model approximating the environment whose time-dependent part, including the control, is fully known. Control alongside Hamiltonian learning of continuous time-independent parameters is addressed through interactions with the system. We demonstrate an order of magnitude advantage in the sample complexity of our method over standard model-free RL in preparing some standard unitary gates with closed and open system dynamics, in realistic numerical experiments incorporating single shot measurements, arbitrary Hilbert space truncations and uncertainty in Hamiltonian parameters. Also, the learned Hamiltonian can be leveraged by existing control methods like GRAPE for further gradient-based optimization with the controllers found by RL as initializations. Our algorithm that we apply on nitrogen vacancy (NV) centers and transmons in this paper is well suited for controlling partially characterised one and two qubit systems.
World models learn the consequences of actions in vision-based interactive systems. However, in practical scenarios like autonomous driving, noncontrollable dynamics that are independent or sparsely dependent on action signals often exist, making it challenging to learn effective world models. To address this issue, we propose Iso-Dream++, a model-based reinforcement learning approach that has two main contributions. First, we optimize the inverse dynamics to encourage the world model to isolate controllable state transitions from the mixed spatiotemporal variations of the environment. Second, we perform policy optimization based on the decoupled latent imaginations, where we roll out noncontrollable states into the future and adaptively associate them with the current controllable state. This enables long-horizon visuomotor control tasks to benefit from isolating mixed dynamics sources in the wild, such as self-driving cars that can anticipate the movement of other vehicles, thereby avoiding potential risks. On top of our previous work, we further consider the sparse dependencies between controllable and noncontrollable states, address the training collapse problem of state decoupling, and validate our approach in transfer learning setups. Our empirical study demonstrates that Iso-Dream++ outperforms existing reinforcement learning models significantly on CARLA and DeepMind Control.
Early stopping based on the validation set performance is a popular approach to find the right balance between under- and overfitting in the context of supervised learning. However, in reinforcement learning, even for supervised sub-problems such as world model learning, early stopping is not applicable as the dataset is continually evolving. As a solution, we propose a new general method that dynamically adjusts the update to data (UTD) ratio during training based on under- and overfitting detection on a small subset of the continuously collected experience not used for training. We apply our method to DreamerV2, a state-of-the-art model-based reinforcement learning algorithm, and evaluate it on the DeepMind Control Suite and the Atari $100$k benchmark. The results demonstrate that one can better balance under- and overestimation by adjusting the UTD ratio with our approach compared to the default setting in DreamerV2 and that it is competitive with an extensive hyperparameter search which is not feasible for many applications. Our method eliminates the need to set the UTD hyperparameter by hand and even leads to a higher robustness with regard to other learning-related hyperparameters further reducing the amount of necessary tuning.
Learning physical dynamics in a series of non-stationary environments is a challenging but essential task for model-based reinforcement learning (MBRL) with visual inputs. It requires the agent to consistently adapt to novel tasks without forgetting previous knowledge. In this paper, we present a new continual learning approach for visual dynamics modeling and explore its efficacy in visual control and forecasting. The key assumption is that an ideal world model can provide a non-forgetting environment simulator, which enables the agent to optimize the policy in a multi-task learning manner based on the imagined trajectories from the world model. To this end, we first propose the mixture world model that learns task-specific dynamics priors with a mixture of Gaussians, and then introduce a new training strategy to overcome catastrophic forgetting, which we call predictive experience replay. Finally, we extend these methods to continual RL and further address the value estimation problems with the exploratory-conservative behavior learning approach. Our model remarkably outperforms the naive combinations of existing continual learning and visual RL algorithms on DeepMind Control and Meta-World benchmarks with continual visual control tasks. It is also shown to effectively alleviate the forgetting of spatiotemporal dynamics in video prediction datasets with evolving domains.
Deep neural networks have been successful in many reinforcement learning settings. However, compared to human learners they are overly data hungry. To build a sample-efficient world model, we apply a transformer to real-world episodes in an autoregressive manner: not only the compact latent states and the taken actions but also the experienced or predicted rewards are fed into the transformer, so that it can attend flexibly to all three modalities at different time steps. The transformer allows our world model to access previous states directly, instead of viewing them through a compressed recurrent state. By utilizing the Transformer-XL architecture, it is able to learn long-term dependencies while staying computationally efficient. Our transformer-based world model (TWM) generates meaningful, new experience, which is used to train a policy that outperforms previous model-free and model-based reinforcement learning algorithms on the Atari 100k benchmark.
Data-driven simulation has become a favorable way to train and test autonomous driving algorithms. The idea of replacing the actual environment with a learned simulator has also been explored in model-based reinforcement learning in the context of world models. In this work, we show data-driven traffic simulation can be formulated as a world model. We present TrafficBots, a multi-agent policy built upon motion prediction and end-to-end driving, and based on TrafficBots we obtain a world model tailored for the planning module of autonomous vehicles. Existing data-driven traffic simulators are lacking configurability and scalability. To generate configurable behaviors, for each agent we introduce a destination as navigational information, and a time-invariant latent personality that specifies the behavioral style. To improve the scalability, we present a new scheme of positional encoding for angles, allowing all agents to share the same vectorized context and the use of an architecture based on dot-product attention. As a result, we can simulate all traffic participants seen in dense urban scenarios. Experiments on the Waymo open motion dataset show TrafficBots can simulate realistic multi-agent behaviors and achieve good performance on the motion prediction task.
Model-based reinforcement learning is one approach to increase sample efficiency. However, the accuracy of the dynamics model and the resulting compounding error over modelled trajectories are commonly regarded as key limitations. A natural question to ask is: How much more sample efficiency can be gained by improving the learned dynamics models? Our paper empirically answers this question for the class of model-based value expansion methods in continuous control problems. Value expansion methods should benefit from increased model accuracy by enabling longer rollout horizons and better value function approximations. Our empirical study, which leverages oracle dynamics models to avoid compounding model errors, shows that (1) longer horizons increase sample efficiency, but the gain in improvement decreases with each additional expansion step, and (2) the increased model accuracy only marginally increases the sample efficiency compared to learned models with identical horizons. Therefore, longer horizons and increased model accuracy yield diminishing returns in terms of sample efficiency. These improvements in sample efficiency are particularly disappointing when compared to model-free value expansion methods. Even though they introduce no computational overhead, we find their performance to be on-par with model-based value expansion methods. Therefore, we conclude that the limitation of model-based value expansion methods is not the model accuracy of the learned models. While higher model accuracy is beneficial, our experiments show that even a perfect model will not provide an un-rivalled sample efficiency but that the bottleneck lies elsewhere.
Model-based reinforcement learning (MBRL) with real-time planning has shown great potential in locomotion and manipulation control tasks. However, the existing planning methods, such as the Cross-Entropy Method (CEM), do not scale well to complex high-dimensional environments. One of the key reasons for underperformance is the lack of exploration, as these planning methods only aim to maximize the cumulative extrinsic reward over the planning horizon. Furthermore, planning inside the compact latent space in the absence of observations makes it challenging to use curiosity-based intrinsic motivation. We propose Curiosity CEM (CCEM), an improved version of the CEM algorithm for encouraging exploration via curiosity. Our proposed method maximizes the sum of state-action Q values over the planning horizon, in which these Q values estimate the future extrinsic and intrinsic reward, hence encouraging reaching novel observations. In addition, our model uses contrastive representation learning to efficiently learn latent representations. Experiments on image-based continuous control tasks from the DeepMind Control suite show that CCEM is by a large margin more sample-efficient than previous MBRL algorithms and compares favorably with the best model-free RL methods.
We propose a novel approach to addressing two fundamental challenges in Model-based Reinforcement Learning (MBRL): the computational expense of repeatedly finding a good policy in the learned model, and the objective mismatch between model fitting and policy computation. Our "lazy" method leverages a novel unified objective, Performance Difference via Advantage in Model, to capture the performance difference between the learned policy and expert policy under the true dynamics. This objective demonstrates that optimizing the expected policy advantage in the learned model under an exploration distribution is sufficient for policy computation, resulting in a significant boost in computational efficiency compared to traditional planning methods. Additionally, the unified objective uses a value moment matching term for model fitting, which is aligned with the model's usage during policy computation. We present two no-regret algorithms to optimize the proposed objective, and demonstrate their statistical and computational gains compared to existing MBRL methods through simulated benchmarks.
We consider the problem of quantifying uncertainty over expected cumulative rewards in model-based reinforcement learning. In particular, we focus on characterizing the variance over values induced by a distribution over MDPs. Previous work upper bounds the posterior variance over values by solving a so-called uncertainty Bellman equation, but the over-approximation may result in inefficient exploration. We propose a new uncertainty Bellman equation whose solution converges to the true posterior variance over values and explicitly characterizes the gap in previous work. Moreover, our uncertainty quantification technique is easily integrated into common exploration strategies and scales naturally beyond the tabular setting by using standard deep reinforcement learning architectures. Experiments in difficult exploration tasks, both in tabular and continuous control settings, show that our sharper uncertainty estimates improve sample-efficiency.
When a vehicle drives on the road, its behaviors will be affected by surrounding vehicles. Prediction and decision should not be considered as two separate stages because all vehicles make decisions interactively. This paper constructs the multi-vehicle driving scenario as a non-zero-sum game and proposes a novel game control framework, which consider prediction, decision and control as a whole. The mutual influence of interactions between vehicles is considered in this framework because decisions are made by Nash equilibrium strategy. To efficiently obtain the strategy, ADP, a model-based reinforcement learning method, is used to solve coupled Hamilton-Jacobi-Bellman equations. Driving performance is evaluated by tracking, efficiency, safety and comfort indices. Experiments show that our algorithm could drive perfectly by directly controlling acceleration and steering angle. Vehicles could learn interactive behaviors such as overtaking and pass. In summary, we propose a non-zero-sum game framework for modeling multi-vehicle driving, provide an effective way to solve the Nash equilibrium driving strategy, and validate at non-signalized intersections.
A key component of model-based reinforcement learning (RL) is a dynamics model that predicts the outcomes of actions. Errors in this predictive model can degrade the performance of model-based controllers, and complex Markov decision processes (MDPs) can present exceptionally difficult prediction problems. To mitigate this issue, we propose predictable MDP abstraction (PMA): instead of training a predictive model on the original MDP, we train a model on a transformed MDP with a learned action space that only permits predictable, easy-to-model actions, while covering the original state-action space as much as possible. As a result, model learning becomes easier and more accurate, which allows robust, stable model-based planning or model-based RL. This transformation is learned in an unsupervised manner, before any task is specified by the user. Downstream tasks can then be solved with model-based control in a zero-shot fashion, without additional environment interactions. We theoretically analyze PMA and empirically demonstrate that PMA leads to significant improvements over prior unsupervised model-based RL approaches in a range of benchmark environments. Our code and videos are available at https://seohong.me/projects/pma/
In Model-based Reinforcement Learning (MBRL), model learning is critical since an inaccurate model can bias policy learning via generating misleading samples. However, learning an accurate model can be difficult since the policy is continually updated and the induced distribution over visited states used for model learning shifts accordingly. Prior methods alleviate this issue by quantifying the uncertainty of model-generated samples. However, these methods only quantify the uncertainty passively after the samples were generated, rather than foreseeing the uncertainty before model trajectories fall into those highly uncertain regions. The resulting low-quality samples can induce unstable learning targets and hinder the optimization of the policy. Moreover, while being learned to minimize one-step prediction errors, the model is generally used to predict for multiple steps, leading to a mismatch between the objectives of model learning and model usage. To this end, we propose \emph{Plan To Predict} (P2P), an MBRL framework that treats the model rollout process as a sequential decision making problem by reversely considering the model as a decision maker and the current policy as the dynamics. In this way, the model can quickly adapt to the current policy and foresee the multi-step future uncertainty when generating trajectories. Theoretically, we show that the performance of P2P can be guaranteed by approximately optimizing a lower bound of the true environment return. Empirical results demonstrate that P2P achieves state-of-the-art performance on several challenging benchmark tasks.
Model based reinforcement learning has proven to be more sample efficient than model free methods. On the other hand, the construction of a dynamics model in model based reinforcement learning has increased complexity. Data processing tasks in radio astronomy are such situations where the original problem which is being solved by reinforcement learning itself is the creation of a model. Fortunately, many methods based on heuristics or signal processing do exist to perform the same tasks and we can leverage them to propose the best action to take, or in other words, to provide a `hint'. We propose to use `hints' generated by the environment as an aid to the reinforcement learning process mitigating the complexity of model construction. We modify the soft actor critic algorithm to use hints and use the alternating direction method of multipliers algorithm with inequality constraints to train the agent. Results in several environments show that we get the increased sample efficiency by using hints as compared to model free methods.
Solving real-world optimal control problems are challenging tasks, as the complex, high-dimensional system dynamics are usually unrevealed to the decision maker. It is thus hard to find the optimal control actions numerically. To deal with such modeling and computation challenges, in this paper, we integrate Neural Networks with the Pontryagin's Maximum Principle (PMP), and propose a sample efficient framework NN-PMP-Gradient. The resulting controller can be implemented for systems with unknown and complex dynamics. By taking an iterative approach, the proposed framework not only utilizes the accurate surrogate models parameterized by neural networks, it also efficiently recovers the optimality conditions along with the optimal action sequences via PMP conditions. Numerical simulations on Linear Quadratic Regulator, energy arbitrage of grid-connected lossy battery, control of single pendulum, and two MuJoCo locomotion tasks demonstrate our proposed NN-PMP-Gradient is a general and versatile computation tool for finding optimal solutions. And compared with the widely applied model-free and model-based reinforcement learning (RL) algorithms, our NN-PMP-Gradient achieves higher sample-efficiency and performance in terms of control objectives.
Cross-Entropy Method (CEM) is commonly used for planning in model-based reinforcement learning (MBRL) where a centralized approach is typically utilized to update the sampling distribution based on only the top-$k$ operation's results on samples. In this paper, we show that such a centralized approach makes CEM vulnerable to local optima, thus impairing its sample efficiency. To tackle this issue, we propose Decentralized CEM (DecentCEM), a simple but effective improvement over classical CEM, by using an ensemble of CEM instances running independently from one another, and each performing a local improvement of its own sampling distribution. We provide both theoretical and empirical analysis to demonstrate the effectiveness of this simple decentralized approach. We empirically show that, compared to the classical centralized approach using either a single or even a mixture of Gaussian distributions, our DecentCEM finds the global optimum much more consistently thus improves the sample efficiency. Furthermore, we plug in our DecentCEM in the planning problem of MBRL, and evaluate our approach in several continuous control environments, with comparison to the state-of-art CEM based MBRL approaches (PETS and POPLIN). Results show sample efficiency improvement by simply replacing the classical CEM module with our DecentCEM module, while only sacrificing a reasonable amount of computational cost. Lastly, we conduct ablation studies for more in-depth analysis. Code is available at https://github.com/vincentzhang/decentCEM
Poor sample efficiency continues to be the primary challenge for deployment of deep Reinforcement Learning (RL) algorithms for real-world applications, and in particular for visuo-motor control. Model-based RL has the potential to be highly sample efficient by concurrently learning a world model and using synthetic rollouts for planning and policy improvement. However, in practice, sample-efficient learning with model-based RL is bottlenecked by the exploration challenge. In this work, we find that leveraging just a handful of demonstrations can dramatically improve the sample-efficiency of model-based RL. Simply appending demonstrations to the interaction dataset, however, does not suffice. We identify key ingredients for leveraging demonstrations in model learning -- policy pretraining, targeted exploration, and oversampling of demonstration data -- which forms the three phases of our model-based RL framework. We empirically study three complex visuo-motor control domains and find that our method is 150%-250% more successful in completing sparse reward tasks compared to prior approaches in the low data regime (100K interaction steps, 5 demonstrations). Code and videos are available at: https://nicklashansen.github.io/modemrl
We apply reinforcement learning (RL) to robotics tasks. One of the drawbacks of traditional RL algorithms has been their poor sample efficiency. One approach to improve the sample efficiency is model-based RL. In our model-based RL algorithm, we learn a model of the environment, essentially its transition dynamics and reward function, use it to generate imaginary trajectories and backpropagate through them to update the policy, exploiting the differentiability of the model. Intuitively, learning more accurate models should lead to better model-based RL performance. Recently, there has been growing interest in developing better deep neural network based dynamics models for physical systems, by utilizing the structure of the underlying physics. We focus on robotic systems undergoing rigid body motion without contacts. We compare two versions of our model-based RL algorithm, one which uses a standard deep neural network based dynamics model and the other which uses a much more accurate, physics-informed neural network based dynamics model. We show that, in model-based RL, model accuracy mainly matters in environments that are sensitive to initial conditions, where numerical errors accumulate fast. In these environments, the physics-informed version of our algorithm achieves significantly better average-return and sample efficiency. In environments that are not sensitive to initial conditions, both versions of our algorithm achieve similar average-return, while the physics-informed version achieves better sample efficiency. We also show that, in challenging environments, physics-informed model-based RL achieves better average-return than state-of-the-art model-free RL algorithms such as Soft Actor-Critic, as it computes the policy-gradient analytically, while the latter estimates it through sampling.
World models power some of the most efficient reinforcement learning algorithms. In this work, we showcase that they can be harnessed for continual learning - a situation when the agent faces changing environments. World models typically employ a replay buffer for training, which can be naturally extended to continual learning. We systematically study how different selective experience replay methods affect performance, forgetting, and transfer. We also provide recommendations regarding various modeling options for using world models. The best set of choices is called Continual-Dreamer, it is task-agnostic and utilizes the world model for continual exploration. Continual-Dreamer is sample efficient and outperforms state-of-the-art task-agnostic continual reinforcement learning methods on Minigrid and Minihack benchmarks.
Model-Based Reinforcement Learning (RL) is widely believed to have the potential to improve sample efficiency by allowing an agent to synthesize large amounts of imagined experience. Experience Replay (ER) can be considered a simple kind of model, which has proved effective at improving the stability and efficiency of deep RL. In principle, a learned parametric model could improve on ER by generalizing from real experience to augment the dataset with additional plausible experience. However, given that learned value functions can also generalize, it is not immediately obvious why model generalization should be better. Here, we provide theoretical and empirical insight into when, and how, we can expect data generated by a learned model to be useful. First, we provide a simple theorem motivating how learning a model as an intermediate step can narrow down the set of possible value functions more than learning a value function directly from data using the Bellman equation. Second, we provide an illustrative example showing empirically how a similar effect occurs in a more concrete setting with neural network function approximation. Finally, we provide extensive experiments showing the benefit of model-based learning for online RL in environments with combinatorial complexity, but factored structure that allows a learned model to generalize. In these experiments, we take care to control for other factors in order to isolate, insofar as possible, the benefit of using experience generated by a learned model relative to ER alone.